摘要翻译：
紧凑型封闭类别为包括量子计算在内的各种重要领域提供了基础形式。这些类别有一个自然的可视化形式的图形。我们给出了关于这类图的等式推理的一种形式，并把它发展成一个具有固定逻辑核的关于紧闭范畴的等式推理的一般证明系统。自动化这一推理过程是由手动图形操作的缓慢和容易出错的性质所驱动的。我们的系统的一个显著特点是，它提供了一个正式的和陈述性的结果的说明，可以包括`椭圆‘式的符号。我们通过实例化量子计算的图形语言来说明这个框架，并说明如何使用它来执行符号计算。
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英文标题：
《Graphical Reasoning in Compact Closed Categories for Quantum Computation》
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作者：
Lucas Dixon and Ross Duncan
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最新提交年份：
2009
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Symbolic Computation        符号计算
分类描述：Roughly includes material in ACM Subject Class I.1.
大致包括ACM学科第一类1的材料。
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一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
  Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for equational reasoning about compact closed categories. Automating this reasoning process is motivated by the slow and error prone nature of manual graph manipulation. A salient feature of our system is that it provides a formal and declarative account of derived results that can include `ellipses'-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.
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PDF链接：
https://arxiv.org/pdf/0902.0514